Signing in iCloud on the web is likely to get easier as Apple is reportedly testing Face ID or Touch ID for authentication.
According to 9to5 Mac, the new sign-in process for iCloud on the web is already available for iOS 13, iPad OS 13, and macOS Catalina beta testers.
If you visit beta.icloud.com on a device running the beta version of the OS, you will see a new pop-up asking if you'd like to sign-in using your Apple ID with biometrics. It doesn't require two-factor confirmation.
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